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Super Bowl coin toss betting: A lesson in value and probability

Super Bowl coin toss betting is a hugely popular proposition bet. This article explains how the legendary coin toss is a great example of the poor value bookmakers offer bettors on a daily basis, and how random events, and probability, can be easily misunderstood.

How the Super Bowl coin toss highlights bad odds

The probability of landing on either side of the Super Bowl coin is 50% - as each outcome has an equal likelihood. This means the odds should be priced at 2.0/2.0 on both sides with zero margin - which it is with Smarkets (0% commission on this market only), meaning bettors statistically have the fairest odds available on the coin toss.

It’s not in the interest of bookmakers or some exchanges to offer the true probability of an event. Instead, they price markets above 100%, creating an edge in their favour. The deviation of the price offered from the ‘true odds’ is the bookmaker's margin.

The odds on the Super Bowl coin toss market provided by bookmakers don't reflect the true probability of the outcomes concerned and are offered as poor as 1.91, which is a 4.7% margin - meaning on average bettors will lose 5p for every pound spent over time on this bet.

Why bettors misunderstand the Super Bowl coin toss

Given the above, it’s intriguing that Super Bowl coin toss betting is such a popular proposition bet, when numerous bookmakers and some exchanges offer such poor value on an even chance event.

Sequential coin flips notoriously generate a false gut feeling, as humans inherently look for patterns, often leading to flawed assumptions.

As an example, let’s say you flip a coin 12 times and it lands on heads every flip. What is the probability that the next toss is heads? The answer is 50%, since the next toss is completely independent of the first 12.

However, when faced with this scenario, many bettors will reason with themselves that since it’s so unlikely to land on heads 13 times in succession, that there is more chance the next flip will be tails. Let’s work out the probability of a coin landing on heads 13 times in succession, when the probability of landing on a head for each of the 13 coin tosses is 50%.

= 1 / 8192= 0.0001220703125 or 0.012%.

Therefore the probability of the coin landing on 13 consecutive heads is very small (0.012%).

However, it’s vital to understand that the previous throws do not affect the probability of the 13th toss being heads.

Bettors can fail to see that the Super Bowl coin (or any coin) has no memory, and that each flip is independent, and therefore streaks are not statistically significant.

This is explained in more detail by the Gambler's Fallacy - a mistaken belief that, if something occurs more frequently than normal during a period, it will happen less frequently in the future, or vice versa. When the situation - such as the Super Bowl coin toss - is random, this belief, as explained above, is false.

In 50 Super Bowls, the coin toss has landed on heads 24 times, and tails 26 times - nearly landing true to its 50/50 probability. The last three Super Bowl coin tosses have landed on tails and been won by the NFC. The flawed betting intuition for Super Bowl 51 would be to give a preference to heads, or the New England Patriots (AFC) winning the toss.

Apply this to betting

The Super Bowl coin toss clearly shows the poor value bookmakers offer bettors on a daily basis, and how some bettors fail to understand random events. Remember a coin has no memory, and the best value to be found is with the fairest odds, which is what you get with Smarkets.